Graduate Management Admission Test (GMAT) Practice Test

What is the ratio of the sides of a 5:12:13 triangle?

1. Right triangle dimensions

2. Odd triangle dimensions

3. Scalene triangle dimensions

4. Isosceles triangle dimensions

The correct answer is: Right triangle dimensions

The correct answer indicates that the triangle defined by the ratio of its sides 5:12:13 is a right triangle. This specific ratio is particularly significant because it corresponds to a Pythagorean triple, which is a set of three positive integers that satisfy the Pythagorean theorem: \(a^2 + b^2 = c^2\). In this case, if we assign the lengths to the sides as 5, 12, and 13, we can compute: \[ 5^2 + 12^2 = 25 + 144 = 169 \] \[ 13^2 = 169 \] Since both expressions yield the same result, this confirms that the triangle with sides in the ratio of 5:12:13 is indeed a right triangle. This property is key to identifying the triangle's classification. While the other options describe different types of triangles—subcategorizing them based on side lengths or angles—none convey the specific and defining characteristic of a right triangle associated with the 5:12:13 ratio. A scalene triangle, for instance, is one where all sides are of different lengths, which this triangle is, but that does not specify its right-angle characteristic